package DMSXL._2024.DP;

public class uniquePaths {
    public static void main(String[] args) {
        System.out.println(new uniquePaths().uniquePaths(3,7));
    }
    public int uniquePaths(int m, int n) {
        //用二维dp数组表示机器人到达某个点的路径条数
        //事实上到达该点只受上面和左面的影响
        int[][] dp = new int[m][n];
        //初始化dp数组
        for (int i = 0; i < n; i++) {
            dp[0][i] = 1;
        }
        for (int i = 0; i < m; i++) {
            dp[i][0] = 1;
        }
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
            }
        }
        return dp[m - 1][n - 1];
    }
}
